基于遗传算法的支持向量机时间序列预测模型优化3

27920069ChineseJournalofScientificInstrumentVol127No19Sep120063(210016),,,,,,O329F201A110.6760OptimizingofsupportvectormachinetimeseriesforecastingmodelparametersbasedongeneticalgorithmsChenGuo(CivilAviationCollege,NanjingUniversityofAeronauticsandAstronautics,Nanjing210016,China)AbstractSupportVectorMachine(SVM)isbasedonStatisticalLearningTheory(SLT)andStructuralRiskMinimizationPrinciple(SRM),andtheoreticallyassuresbestmodelgeneralization.Therefore,itismoreper2fectintheorythanArtificialNeuralNetwork(ANN)thatisbasedonEmpiricalRiskMinimizationPrinciple(ERM).Inthispaper,SVMisusedtoestablishtimeseriesforecastingmodel,studytheparametersthatinflu2enceforecastingaccuracy.Onthebasisofanalyzingmodelparameters’influence,aself2adaptiveoptimizingal2gorithmforestablishingthemodelparametersbasedongeneticalgorithmisputforward.Intheend,examplesshowingthecorrectnessandvalidityoftheproposedalgorithmaregiven.Keywordssupportvectormachine(SVM)timeseriesanalysisforecastinggeneticalgorithmoptimizing1,,,ARMA(n,m)[1],,,,ARMA,[223],,[4],V.Vapnik[4],,[526],,,,C,,,3200579:10812[7],,,,,,{x(t)}(t=1,2,,N),m:x(t+)=f{x(t),x(t-),,x(t-(m-1))},:m,,Takens[8]:d,m2d+1,,,,,,,m,,{x1,x2,},m,:xn+1=F(xn,xn-1,,xn-m+1)(1)(1)F3,(xi,yi),xRd,yiR,i=1,,n,:f(x)=(wx)+b(2):wRd;bR;(wx)wx,:Q(w)=12(ww)+CRemp(f)(3):C,;Remp(f),HuberLaplace-,-,,:L(d,y)=|d-y|-,|d-y|0,(4)-,(3):Q(w)=12(ww)+C1nni=1|yi-f(xi)|(5),|yi-(wxi)-b|(i=1,2,,n),f(x)+f(x)-,1,:min12(ww)s.tyi+(wxi)-b,(wxi)-yi+b(6)1,030,(6):min12(ww)+Cni=1(i+3i)s.tyi-(wxi)+b+i,(wxi)-yi+b+3i(7)i3i:Q(,3)=ni=1yi(i-3i)-ni=1(i+3i)-12ni=1,j=1(i-3i)(j-3j)(xixj)s.tni=1(i-3i)=0,0iC,i=1,2,,n,03iC,i=1,2,,n(8)j3i,:b=-1/2ni=1(i-3i)((xi,xt)+(xi,xs))(9)b,,xsxt2:f(,3,x)=ni=1(i-3i)(x,xi)+b(10)K(xi,xj),,,(8):Q(,3)=ni=1yi(i-3i)-ni=1(i+3i)-12ni=1,j=1(i-3i)(j-3j)K(xixj)(11)108227(10):f(,3,x)=ni=1(i-3i)K(x,xi)+b(12),,n-1,xt={xt-1,xt-2,,xt-p}xt:f:RP-R,,p:X=x1x2xn-px2x3xn-p+1xpxp+1xn-1Y=xp+1xp+2xn=yp+1yp+2yn(13)(13):yt=n-pi=1(i-3i)k(xi,xt)+b,t=p+1,,n(14)44.1,{x1,x2,},,,,,,(averagerelativevariance,ARV)[9],:ARV=Ni=1[x(i)-^x(i)]2/Ni=1[x(i)-…x(i)]2(15):N,x(i),Šx,^x(i),ARV,,ARV=0,ARV=1,,N,ARVSVM4.2SVM,,17001987,1/5SVM,4.3,,,,,:pC(1)p:;(2),,,,(0.00010.1);(3)C,CC(11000000);(4),,,,(29);,(0.13.8),,Np1414,,,1CCNppARV10.01290.2320100.01290.73411000.0129163.3210000.012917820100000.0129797852CNppARV10.1290.204010.01290.232010.001290.245010.0001290.245110.00001290.24503NpCNppARV10.01190.253410.01290.232010.01390.466010.01490.914710.01591.51479:10834pCNppARV10.01210.528510.01230.216510.01250.390210.01270.413410.01290.23205,CNpp,SVM,CNpp,,[10],,SVM,SVMCNpp,,,CNpp,SVM,ARV,,,,,,:0.500.05()CNpppNpC,n1n2n3n4,n1+n2+n3+n4,2n1+n2+n3+n40,,1pNp,C,C,C=10CC,,=0.1ARV,,f=1/ARV6(1):20%:0.500.0510,10pNpCn1=4n2=2n3=2n4=210:p=9Np=2C=1=0.019.6896,ARV0.232022SVM(2):,,50%:0.500.0530,10pNpCn1=2n2=2n3=2n4=210:p=4Np=1C=1=0.0013.2505,ARV0.30763,3SVM7;SVM4:pNpC,4SVM(pNpC),SVM108427[1],.[M].:,1991.[2]FARBERLA.Nonlinearsignalprocessingusingneuralnetwork:Predictionandsystemmodeling[R].Techni2calReportLA2UR28722662,LosAlamosNationalLabo2ratory.LosAlamos.NM,1987.[3]WEIGENDAB.Predictingthefuture:aconnectionistapproach[J].InternationalJournalofNeuralSystem,1990(1):1932209.[4]VAPNIKV.Thenatureofstatisticallearning[M].NewYork:Springer,1995.[5]TAYFEH,CaoLJ.Applicationofsupportvectormachinesinfinancialtimeseriesforecasting[J].Ome2ga,2001,29:3092317.[6],,,.[J].,2003,18(6):3932397.[7]FORDJ.Chaosatrandom[J].Natrue,1983,305(20):17224.[8]TAKENSF.Detectingstrangeattractorsinturbulence[C].In:Rand,D.A.,Young,L.S.DynamicalSystemsandTurbulence,Berlin:Springer2Verlag,1981.[9]CHOLEWOT,ZURADAJM.Sequentialnetworkcon2structionfortimeseriesprediction[C].ProceedingsoftheIEEEInternationalJointConferenceonNeuralNet2works,1997:203422039.[10]GOLDBERGD.Geneticalgorithmsinsearch,optimiza2tionandmachinelearning[M].Addison2Wesley,Read2ing,MA,1989.1972E2mail:[e-mail]